Question

In Exercise 4.12, we give linear equations. For each equation,

a. find the $y$-intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

Given equation is,

$y=-3x$

Short answer

a. $y$-intercept is $0$and slope is $-3$

b. Slope is downward.

c. The graph is given below.

Step-by-step solution

Part(a) Step 1: Given information

We need to find $y$-intercept and slope of given linear equation.

Part(a) Step 2: Calculations

General form of linear equation is $y=mx+c$where $m$is slope and $c$is y-intercept.

Comparing $y=-3x+0$ with general form we get,

slope $m=-3$

y-intercept$c=0$

Part(b) Step 1: Given information

We have to determine the direction of slope of given linear equation.

Part(b) Step 2: Answer and its explanation

As we see the slope is having negative sign so the slope will point in downward direction.

Part(c) Step 1: Given information

We have to graph the equation.

Part(c) Step 2: Explanation

Graph for above linear equation is